Particle Filter

Other names

What is it good for? Key idea?

particle ﬁlters estimate the posterior probability density over the state space of a dynamic system

key idea of this technique is to represent probability densities by sets of samples

“The efﬁciency of particle ﬁlters lies in the way they place computational resources. By sampling in proportion to likelihood, particle ﬁlters focus the computational resources on regions with high likelihood, where good approximations are most important.” (Dieter Fox)

resampling is done by a Monte-Carlo approach –> particle filter = probabilistic algorithm: we draw randomly samples from the current pdf according to the particle weights

particles that can explain the measurement gain weight

particles that cannot explain the measurement loose weight

“filtering” refers to determining the distribution of a latent variable at a specific time, given all observations up to that time

Relation to Bayes Filtering?

particle filters can be seen as a sample-based implementation of Bayes filtering

key idea of Bayes ﬁltering is to recursively estimate the posterior probability density over the state space conditioned on the data collected so far

Bayes ﬁlters are an abstract concept in that they only provide a probabilistic framework for recursive state estimation. To implement Bayes ﬁlters, one has to specify the perceptual model p(z_t |x_t), the dynamics p(x_t | x_t−1 , u_t−1), and the representation of the belief Bel(x_t)

where x_t is the state at time t, u_t is a control measurement, and z_t is an observation